One of the most mysterious aspects of Saito’s theory of Hodge modules are the Hodge and weight filtrations that accompany the pushforward of a Hodge module under an open embedding. In this paper we consider the open embedding in a product of complementary Grassmannians given by pairs of transverse subspaces. The push-forward of the structure sheaf under this open embedding is an important Hodge module from the viewpoint of geometric representation theory and homological knot invariants. We compute the associated graded of this push-forward with respect to the induced Hodge filtration as well as the resulting weight filtration. The main tool is a categorical sl2 action on the category of Dh-modules on Grassmannians. Along the way we also clarify the interaction of kernels for Dh-modules with the associated graded functor. Both of these results may be of independent interest.
ASJC Scopus subject areas
- Physics and Astronomy(all)